英文标题：
《Regularity properties in a state-constrained expected utility
  maximization problem》
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作者：
Mourad Lazgham
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最新提交年份：
2015
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英文摘要：
  We consider a stochastic optimal control problem in a market model with temporary and permanent price impact, which is related to an expected utility maximization problem under finite fuel constraint. We establish the initial condition fulfilled by the corresponding value function and show its first regularity property. Moreover, we can prove the existence and uniqueness of optimal strategies under rather mild model assumptions. On the one hand, this result is of independent interest. On the other hand, it will then allow us to derive further regularity properties of the corresponding value function, in particular its continuity and partial differentiability. As a consequence of the continuity of the value function, we will prove the dynamic programming principle without appealing to the classical measurable selection arguments.
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中文摘要：
我们考虑了一个具有暂时和永久价格影响的市场模型中的随机最优控制问题，该问题与有限燃料约束下的期望效用最大化问题有关。我们建立了相应的值函数满足的初始条件，并证明了它的第一个正则性。此外，我们可以在相当温和的模型假设下证明最优策略的存在性和唯一性。一方面，这个结果具有独立的意义。另一方面，它将允许我们进一步推导相应值函数的正则性性质，尤其是其连续性和部分可微性。由于值函数的连续性，我们将证明动态规划原理，而不诉诸经典的可测选择参数。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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